Delhi cruised home on 2-161 with 11 balls to spare after Rajasthan had struggled to reach 6-160, with Warner, playing the anchor role, guiding them to victory after Marsh's early good fortune was followed by dazzling pyrotechnics.
Marsh blasted 89 and Warner made an unbeaten 52 as they shared a 144-run second-wicket stand after Trent Boult had removed opener Srikar Bharat off the second ball.
Boult could have made it 2-2 when it appeared he'd trapped Marsh lbw first ball but was given not out.
Rajasthan didn't go for a referral, but the television replay then suggested the New Zealand fast bowler's perfect yorker had actually hit the Aussie's boot first before the bat.
"I honestly thought I smashed it first so I wasn't worried," Marsh said on getting an early reprieve before hitting seven sixes and five fours.
"It was lucky as I look guilty when I know I'm gone. I did feel I got away with it!"
Both batters survived Boult's brilliant three-over spell before dominating the bowlers midway through the innings. Rajasthan held back key spinner Yuzvendra Chahal until the ninth over but luck continued to favour Delhi.
Jos Buttler couldn't grab Warner's difficult running catch at long-off in Chahal's first over which also saw a sharp turning delivery hitting the leg stump of the opener's leg stump but the bails didn't come off the groove.
Both batters then cut loose in the death overs and even smashed Boult for 15 runs in his last over.
Chahal finally broke the stand when Marsh holed out at short fine leg while top-edging a sweep before Rishabh Pant smashed two sixes against the legspinner, who finished with 1-43.
Earlier, Marsh had also picked up 2-25 and restricted Rajasthan's total which mae him a worthy player of the match.
Ravichandran Ashwin scored 50 off 38 at No.3 before Marsh, crucially, dismissed him while run-machine Buttler's (7) dismissal in the third over pushed back Rajasthan's bid to score freely in the batting powerplay.
